Collaborative spectrum sensing based on the ratio between largest eigenvalue and Geometric mean of eigenvalues

Muhammad Zeeshan Shakir, Anlei Rao, Mohamed-Slim Alouini

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In this paper, we introduce a new detector referred to as Geometric mean detector (GEMD) which is based on the ratio of the largest eigenvalue to the Geometric mean of the eigenvalues for collaborative spectrum sensing. The decision threshold has been derived by employing Gaussian approximation approach. In this approach, the two random variables, i.e. the largest eigenvalue and the Geometric mean of the eigenvalues are considered as independent Gaussian random variables such that their cumulative distribution functions (CDFs) are approximated by a univariate Gaussian distribution function for any number of cooperating secondary users and received samples. The approximation approach is based on the calculation of exact analytical moments of the largest eigenvalue and the Geometric mean of the eigenvalues of the received covariance matrix. The decision threshold has been calculated by exploiting the CDF of the ratio of two Gaussian distributed random variables. In this context, we exchange the analytical moments of the two random variables with the moments of the Gaussian distribution function. The performance of the detector is compared with the performance of the energy detector and eigenvalue ratio detector. Analytical and simulation results show that our newly proposed detector yields considerable performance advantage in realistic spectrum sensing scenarios. Moreover, our results based on proposed approximation approach are in perfect agreement with the empirical results.
Original languageEnglish
Title of host publicationIEEE GLOBECOM Workshops (GC Wkshps), 2011
Place of PublicationHouston, TX, USA
PublisherIEEE
Pages913-917
Edition2011
ISBN (Electronic)978-1-4673-0040-7, 978-1-4673-0038-4
ISBN (Print)978-1-4673-0039-1
DOIs
Publication statusPublished - 2011
Externally publishedYes

Publication series

NameIEEE GLOBECOM Workshops (GC Wkshps)
PublisherIEEE
ISSN (Print)2166-0077

Keywords

  • Spectrum sensing
  • Geometric mean detector (GEMD)
  • moments of largest eigenvalue
  • moments of Geometric mean of eigenvalues
  • Gaussian approximation approach

Cite this

Shakir, M. Z., Rao, A., & Alouini, M-S. (2011). Collaborative spectrum sensing based on the ratio between largest eigenvalue and Geometric mean of eigenvalues. In IEEE GLOBECOM Workshops (GC Wkshps), 2011 (2011 ed., pp. 913-917). (IEEE GLOBECOM Workshops (GC Wkshps)). Houston, TX, USA: IEEE. https://doi.org/10.1109/GLOCOMW.2011.6162590
Shakir, Muhammad Zeeshan ; Rao, Anlei ; Alouini, Mohamed-Slim. / Collaborative spectrum sensing based on the ratio between largest eigenvalue and Geometric mean of eigenvalues. IEEE GLOBECOM Workshops (GC Wkshps), 2011. 2011. ed. Houston, TX, USA : IEEE, 2011. pp. 913-917 (IEEE GLOBECOM Workshops (GC Wkshps)).
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abstract = "In this paper, we introduce a new detector referred to as Geometric mean detector (GEMD) which is based on the ratio of the largest eigenvalue to the Geometric mean of the eigenvalues for collaborative spectrum sensing. The decision threshold has been derived by employing Gaussian approximation approach. In this approach, the two random variables, i.e. the largest eigenvalue and the Geometric mean of the eigenvalues are considered as independent Gaussian random variables such that their cumulative distribution functions (CDFs) are approximated by a univariate Gaussian distribution function for any number of cooperating secondary users and received samples. The approximation approach is based on the calculation of exact analytical moments of the largest eigenvalue and the Geometric mean of the eigenvalues of the received covariance matrix. The decision threshold has been calculated by exploiting the CDF of the ratio of two Gaussian distributed random variables. In this context, we exchange the analytical moments of the two random variables with the moments of the Gaussian distribution function. The performance of the detector is compared with the performance of the energy detector and eigenvalue ratio detector. Analytical and simulation results show that our newly proposed detector yields considerable performance advantage in realistic spectrum sensing scenarios. Moreover, our results based on proposed approximation approach are in perfect agreement with the empirical results.",
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Shakir, MZ, Rao, A & Alouini, M-S 2011, Collaborative spectrum sensing based on the ratio between largest eigenvalue and Geometric mean of eigenvalues. in IEEE GLOBECOM Workshops (GC Wkshps), 2011. 2011 edn, IEEE GLOBECOM Workshops (GC Wkshps), IEEE, Houston, TX, USA, pp. 913-917. https://doi.org/10.1109/GLOCOMW.2011.6162590

Collaborative spectrum sensing based on the ratio between largest eigenvalue and Geometric mean of eigenvalues. / Shakir, Muhammad Zeeshan; Rao, Anlei; Alouini, Mohamed-Slim.

IEEE GLOBECOM Workshops (GC Wkshps), 2011. 2011. ed. Houston, TX, USA : IEEE, 2011. p. 913-917 (IEEE GLOBECOM Workshops (GC Wkshps)).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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AB - In this paper, we introduce a new detector referred to as Geometric mean detector (GEMD) which is based on the ratio of the largest eigenvalue to the Geometric mean of the eigenvalues for collaborative spectrum sensing. The decision threshold has been derived by employing Gaussian approximation approach. In this approach, the two random variables, i.e. the largest eigenvalue and the Geometric mean of the eigenvalues are considered as independent Gaussian random variables such that their cumulative distribution functions (CDFs) are approximated by a univariate Gaussian distribution function for any number of cooperating secondary users and received samples. The approximation approach is based on the calculation of exact analytical moments of the largest eigenvalue and the Geometric mean of the eigenvalues of the received covariance matrix. The decision threshold has been calculated by exploiting the CDF of the ratio of two Gaussian distributed random variables. In this context, we exchange the analytical moments of the two random variables with the moments of the Gaussian distribution function. The performance of the detector is compared with the performance of the energy detector and eigenvalue ratio detector. Analytical and simulation results show that our newly proposed detector yields considerable performance advantage in realistic spectrum sensing scenarios. Moreover, our results based on proposed approximation approach are in perfect agreement with the empirical results.

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Shakir MZ, Rao A, Alouini M-S. Collaborative spectrum sensing based on the ratio between largest eigenvalue and Geometric mean of eigenvalues. In IEEE GLOBECOM Workshops (GC Wkshps), 2011. 2011 ed. Houston, TX, USA: IEEE. 2011. p. 913-917. (IEEE GLOBECOM Workshops (GC Wkshps)). https://doi.org/10.1109/GLOCOMW.2011.6162590